A commonly used technique for evaluating formations surrounding an earth borehole is resistivity logging. A porous formation having a high resistivity generally indicates the presence of hydrocarbons, while a porous formation with low resistivity generally indicates water saturation, for example.
Modern induction resistivity logging tools operate by transmitting a signal from a transmitter station and measuring the voltage of the received signal at a receiver station. These voltages are referred to as transimpedance coupling voltages and are sensitive to the formation properties, such as horizontal and vertical conductivities, relative dip angle, and the dip azimuthal direction, rendering such induction logging tools capable of delivering a data from which a variety of useful information about the formation can be extracted and estimated.
These transimpedance coupling voltages, however, are also sensitive to borehole and tool properties, such as mud conductivity, hole diameter, tool eccentering distance, and tool eccentering azimuthal angle. Thus, the transimpedance coupling voltages are corrected for the borehole and tool properties. Mud conductivity and hole diameter can easily be measured, and in many cases are already known, so compensation for these borehole properties is relatively straightforward. Measuring tool eccentering distance and tool eccentering azimuthal angle is difficult as those parameters are in constant flux during drilling. For modern single-axis induction resistivity logging tools, the sensitivity to tool eccentering distance and tool eccentering azimuthal angle is minimal enough such that it can effectively be ignored and an inversion can be performed to achieve accurate results.
In the case where a multi-axial induction resistivity logging tool is used, the sensitivity to tool eccentering distance and tool eccentering azimuthal angle for some axes is large. Since the tool eccentering distance and tool eccentering azimuthal angle is constantly changing, compensating for such constantly changing conditions is difficult. However, the result of not compensating is that the results for some axes are unacceptable inaccurate.
Consequently, a method of estimating borehole and formation properties that overcomes this difficult is commercially desirable.